Abstract
The systems studied are equivalent to indefinite cylinders with rotationally symmetrical potentials. The analytical expressions for the derivatives of the axial potential with respect to z are given for two elementary systems called "Electrode" and "Interval." This analysis is also applied to one further elementary system in which the boundary potential is zero except in one region where its dependence on z follows a second-order polynomial. For a complex real system, the analytical expressions of the derivatives of the axial potential are obtained by superposition of elementary systems. This method renders possible a rapid calculation of the field, even for systems with large electrode separations. Furthermore, it may be used for the design of aberration-corrected systems.[Journal translation]
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